objectSuccess is of type T. That's exactly what Action<T> success expects as parameter. No conversion is required.

You can think of success as being a method declared like this:

void success(T arg)
{
}

And as Jorn Vernee says, remove <T> from Success<T>. You don't need a generic type parameter for this method, as it uses the generic type parameter of the class. If for some reason you need different generic type parameters for class and method, you must give them different names. But that's not the case here.